Crystal controlled oscillators are frequently used as a time or frequency reference due to their long term stability. In most such applications, a quartz crystal is connected in series with an amplifier, providing energy to sustain oscillation of the crystal at its resonance frequency. The output of the amplifier is also connected to a system requiring the stability of the reference frequency output from the oscillator.
An equivalent circuit for a quartz crystal includes an inductor, L, a resistance, R, and a capacitance, C, all connected in series; in addition, the preceding series connected elements are connected in parallel with a capacitor, C.sub.0. The stability of the resonant frequency and operating phase of the crystal directly depend on the relative stability of these four equivalent circuit elements. In a tuned quartz crystal oscillator, the four equivalent circuit elements tend to be very stable, and their stability may be further enhanced by mounting the crystal in an evacuated housing, and placing it in a temperature controlled environment. However, a quartz crystal may be used in applications in which it cannot be environmentally controlled, and in which the relative stability of the equivalent circuit elements is more likely to vary than is the case with more conventional tuned crystal oscillators. Such is the case when a crystal having a high mechanical Q is used for sensing force.
U.S. Pat. No. 4,215,570 discloses an improved design for a force sensing crystal having a relatively high Q of approximately 100,000 (a high Q insures that less external energy must be supplied to sustain the crystal oscillations and that the crystal will have a more stable resonant frequency). The crystal in this force sensor is shaped like a double-ended tuning fork, i.e., it is divided into two end portions connected by two wide bars separated by a narrow slot. Each bar is excited into vibration by electrical contacts or pads carried thereon, in conjuction with an appropriate oscillating circuit. The frequency of the vibration is a function of the magnitude of the force transmitted from the end portions to the bars. In relating the force sensing crystal to the equivalent circuit elements described above, the value of L corresponds to the mass of the tuning fork tines, i.e. The mass of the wide bars, and the density of the surrounding gas. The value of C is determined by the stiffness of the tines, while R relates to the damping of the vibrational motion. The real capacitance between the electrodes carried on the tines is represented by C.sub.0.
In a typical tuned crystal oscillator, the phase response of the crystal is directly related to the frequency of oscillation, such that the loop gain is exactly one at a phase angle of zero degrees. Since a crystal oscillator includes both a piezoelectric crystal and its associated electronic circuit, any deviation from zero phase angle in the crystal must be offset by the circuit. thus, if the crystal operates at a complex admittance, Y, at a phase angle, .theta., the electronics must operate with a transimpedance of 1/Y, at a phase angle, -.theta..
When a piezoelectric crystal is cut as described in the above-referenced referenced patent and geometrically optimimized to sense force, its dynamic equivalent series resistance, R, becomes substantially greater than that of a crystal used in a conventional tuned oscillator. The value of R corresponds to the damping of the crystal's vibration or the amount of energy lost by the crystal per cycle of vibration. In a force sensing crystal, R can vary due to changes in: (a) the energy lost to the lattice structure of the crystal; (b) energy lost to the gas surrounding the crystal; and (c) energy lost to the pads on which the crystal is mounted, i.e. energy dissipated in the force sensor assembly.
The phase response of a force sensing crystal admittance at a frequency, .omega., may be expressed in terms of the crystal equivalent circuit parameters, as follows: ##EQU1##
From equation 1, it will be apparent that .theta..sub.y (.omega.) is dependent upon all the equivalent circuit parameters and .omega.. The parameters C.sub.0 and L are generally relatively stable in a force sensing crystal; however, as already explained, the damping or energy loss, R, is subject to variation, and the value, C, changes as a function of the applied force. Further, a shift in the phase response due to a change in R will cause the oscillation frequency of the crystal to change. Any change in the crystal frequency that is not caused by a variation in the force which the crystal is sensing will cause an error in the output signal produced by the force sensing transducer comprising the crystal. This problem is particularly manifest in force sensing crystals having a high Q and operated in a gas environment rather than a vacuum.
Accordingly, it is an object of the present invention to decouple changes in damping or energy loss in a force sensing crystal from the phase response and frequency of the crystal. A further object is to provide a circuit which compensates for changes in admittance and phase response of the crystal. These and other objects and advantages of the invention will be apparent from the attached drawings and the description of the preferred embodiment that follows.